On reconstructing photon statistics by on/off detectors: Toward the multi-partite case

The propagation of pulses of the pump and its second harmonic in a quadratically nonlinear medium whose linear properties are characterized by a negative refractive index at the pump frequency and by a positive refractive index at the harmonic frequency is considered theoretically. In the case of a low intensity of the interacting waves, the pump and second-harmonic pulses propagate in the opposite directions, but sufficiently powerful pulses can form a simulton—a solitary two-frequency wave propagating in a certain direction as a single whole. Solutions to a set of equations are found which describe the steady-state propagation of a solitary wave and of a nonlinear periodic (cnoidal) wave.     

Third harmonic generation in the field of a backward pump wave

Third harmonic generation in a nonlinear medium the refractive index of which is negative at the pump frequency and positive at the harmonic frequency with allowance for self-action effects is considered theoretically. An exact solution of equations that describe the parametric interaction of continuous waves has been obtained analytically. The behavior of the solution is analyzed depending on the degree of violation of the phase matching condition. It is shown that, in a definite domain of values of nonlinear susceptibilities of the third order, there exists a critical value of the phase detuning at which the monotonic transform of the pump into the harmonic is changed by a periodical one. This phenomenon does not occur when the third harmonic is generated in ordinary media with a positive refractive index.     

Spatial distribution of the interacting Waves’ amplitudes under third harmonic generation in a negative-positive refractive medium

The process of third harmonic generation in a cubically nonlinear medium that is negatively refractive at the fundamental frequency and positively refractive at the third harmonic frequency is considered. For the stationary case, the amplitude distribution was obtained for waves interacting inside a sample for different values of phase mismatch. In the periodic regime of generation, it is shown that the amplitude of the fundamental wave inside the medium can exceed its value at the input, which is impossible in the standard case of harmonic generation in a medium positively refractive at both frequencies. The influence of energy losses in the sample on the spatial distribution of waves’ amplitudes of both frequencies has been studied.     

Interaction of spatially modulated pump and FIR waves in Raman laser

The propagation of spatially modulated IR pump and FIR generated waves interacting in the active gas medium of Raman laser is simulated numerically. Stationary nonlinear diffraction of monochromatic beams is studied for the isolated homogeneously broadened three-level system without any limitations on the values of field strength and frequency offset. It is shown that FIR radiation is trapped in the active wave guide induced owing to the nonlinear refractive index mechanism and gain inhomogeneity across the pump wave beam. Nonlinear focus positions and on-axis focal intensities for both fields are calculated.     

Moving near-gap solitons in the nonlinear optical medium

For a one-dimensional nonlinear optical medium with a periodic refraction index, new two-parameter soliton solutions of electrodynamics equations have been found. These solutions represent two interacting waves that propagate in two opposite directions. The oscillation frequency of each wave may fall either into the forbidden gap in the linear spectrum or outside it, and the group velocity may vary from zero to a maximal value that is determined by the parameters of the medium. Algebraic soliton solutions have been found as the limit of the nonlinear solutions, when the nonlinear wave frequency tends to the frequency of one of the linear-spectrum branches.     

Pulse propagation in four-wave mixing process with group index difference of signal and idler waves

Four-wave mixing process with a large group index difference of the signal and idler pulses in a nonlinear optical fiber is theoretically investigated when the pump is continuous light. We prove that in the four-wave mixing process, the signal and idler waves would finally propagate in a common group velocity in spite of their different group indices. When the effective phase mismatch in four-wave mixing is not zero, their carrier frequencies shift in different directions. The asymptotic result of the signal and idler shape and carrier frequency shift are obtained. The theoretical prediction is validated by the numerical simulation.     

Long wave-short wave resonance in nonlinear negative refractive index media

We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.     

Simultaneous fs pulse spectral broadening and third harmonic generation in highly nonlinear fibre: experiments and simulations

Experiments and numerical simulations are used to study non-phasematched single-mode third harmonic generation occurring simultaneously with fs pulse spectral broadening in highly nonlinear fibre. Pump pulses around 100 fs at 1560 nm injected into sub-5 cm lengths of commercially-available highly nonlinear fibre are observed to undergo spectral broadening spanning over 700 nm at the -30 dB level, and to simultaneously generate third harmonic radiation around 520 nm. Simulations based on a generalized nonlinear envelope equation are shown to well reproduce the spectral structure of the broadened pump pulses and the generated third harmonic signal. PACS 42.65.-k; 42.81.Dp     

TEMPORAL OPTICAL SOLITONS VIA MULTISTEP χ(2) CASCADING

We consider a multistep χ⁽²⁾ cascading for light pulses with the dispersion of the system taken into account. Using the method of multiple scales we derive a set of coupled envelope equations governing the nonlinear evolution of the fundamental, second and third harmonic waves involved simultaneously in two nonlinear optical processes, i.e. second harmonic generation and sum frequency mixing. We show that three-wave temporal optical solitons are possible in three-and four-step cascading in the presence of a group-velocity mismatch between different pulses.     

Effect of the group velocity mismatch and dispersion of nonlinear susceptibility on the modulation instability of electromagnetic waves in a medium with quadratic nonlinearity

Modulation instability of continuous plane waves of the pump beams and the second harmonic that are described by the set of equations for the process of second-harmonic generation with allowance made for the dispersion of nonlinear susceptibility is considered. The case of type I phase matching is analyzed. In the regions of anomalous and normal group velocity dispersion, the instability increments are determined as functions of the frequency and the wave numbers of perturbations. It was found that the difference in the group velocities of the interacting waves exerts the most substantial effect on the evolution of the modulation instability.     

Tunable control of the frequency correlations of entangled photons

We experimentally demonstrate a new technique to control the type of frequency correlations of entangled photon pairs generated by spontaneous parametric downconversion. Frequency-correlated and frequency-anticorrelated photons are produced when a broadband pulse is used as a pump. The method is based on the control of the group velocities of the interacting waves and can be applied in any nonlinear medium and frequency band of interest.     

Polarization-Dependent Phase-Conjugate Reflectivity in Randomly Oriented Saturable Absorbers: Effects of Direction of Transition Dipole Moment Associated with Excited-State Absorption

The effects of the direction of transition dipole moment on polarization-dependent phase-conjugate (PC) reflectivity by degenerate four-wave mixing in a saturable-dye-doped film are theoretically investigated. On the basis of a four-energy-level model for the saturable dyes, the pump-intensity dependence of the PC reflectivity is calculated for the two cases of a probe wave being polarized either parallel or perpendicular to pump waves, when the transition dipole moment associated with excited-state absorption tilts from that associated with ground-state one. For the parallel polarization, in the case of two transition dipole moments having different directions, a dip appears in the PC reflectivity curve near a resonant frequency on account of the characteristics of nonlinear absorption, whereas it disappears when the frequency of light is off resonance due to the influence of nonlinear refractive index.     

Passive mode-locking upon limitation of the spectral width of a laser emission

An analysis is presented of passive locking of modes in lasers with an additional intracavity element that limits the spectral width of a laser emission due to frequency dispersion of an order higher than quadratic. It is found that spectral limitation of this type may give rise to a multiple-pulse regime of passive mode-locking. The laser mode of operation established after a transient process, in this case, appears to be multistable, with the number of pulses per axial period being dependent on the initial conditions of the lasing. It is shown that the dependence of the number of pulses on the pump power is of hysteretic character. The theoretical analysis and numerical simulation are carried out using an equation close to the Ginzburg-Landau equation. Specifically, the nonlinear losses and nonlinear refractive index are supposed to be inertia-less and proportional to the light intensity; the frequency dispersion of the gain and the refractive index are approximated by a quadratic dependence; and the frequency-dependent losses related to the additional spectral limitation of the laser emission are determined by fourth-order frequency dispersion. The possibility of using the characteristic features of mode-locking predicted for control of regimes of formation and propagation of ultrashort light pulses is discussed.     

Symbolic computation on pulse compression without pedestal in an inhomogeneous medium

The coupled nonlinear Schrödinger equations with the harmonic potential and variable coefficients are studied for the pulse propagation in an inhomogeneous medium. With the modified Hirota method and symbolic computation, the bilinear form and analytic one-soliton solutions are obtained. A type of pulse compression technique is proposed, which can have the optical pulses compressed without any external devices. Moreover, the compressed pulses are pedestal free. The influences of the inhomogeneity of the refractive index, Kerr nonlinearity and diffraction are analyzed as well. The proposed technique may provide a different method for the pulse compression.     

Phase effects at second harmonic generation of powerful laser radiation in noncentrosymmetrical media

There has been developed the theory of second harmonic generation of the intensive laser fields in the existence of both quadratic and cubic polarization in medium in the constant-intensity approximation accounting for the reverse effect of the excited wave on the exciting one and simultaneously allowing us to take into account phase mismatch and the damping of all the interacting waves. It is shown that the changes of pump intensity through self-phase and cross-phase modulation processes effect optimum phase relationship between interacting waves, the change of the spatial beating period. The conditions of compensating undesirable phase shifts between interacting waves have been determined, the analytical expressions for calculation of optimum values of phase mismatch, length of noncentrosymmetrical medium and the spatial beating period are offered. It is shown that in the absence of linear phase mismatch with an increase of basic radiation intensity the spatial beating period is being reduced. The numerous analysis has been made of frequency doubling process efficiency for KDP and LiNbO₃ crystals.     

Phase relations between focused bichromatic laser pulses in terahertz wave generation from gas plasma

Terahertz emission from air excited by the tightly focused fundamental and second harmonic pulses of femtosecond Ti:Sapphire laser has been analyzed. It has been found that the curved phase fronts of the pump waves cancel each other resulting in the flat phase front of the nonlinear polarization at terahertz frequency. Also, in addition to the phase terms obtained using plane-wave approximation, we have found the yet unreported phase term, which in most cases can be as large as π/2.     

Phase matched vectorial three-wave mixing in isotropic Kerr media

A theoretical analysis of vectorial three-wave mixing in isotropic Kerr media is presented. The analysis based on the coupled-wave equations describes the amplification of a weak wave by coupling with a strong pump wave phase matched by optically induced change of average refractive index. The phase matching condition for interacting waves with different polarizations is calculated, allowing a large amplification of a weak wave by three-wave mixing in thick Kerr media. The main conclusions of our theoretical analysis are supported by the results of experiments in CS₂ liquid medium.     

Propagation of elliptically polarized laser pulses in isotropic gyrotropic medium with relaxation cubic nonlinearity and anomalous frequency dispersion

The self-action of elliptically polarized Gaussian laser pulses in an isotropic gyrotropic medium with an anomalous frequency dispersion and cubic Kerr nonlinearity with a finite relaxation time on the order of the pulse duration is numerically studied. It is shown that, at the output of the medium, the pulse polarization nonmonotonically varies with time. The main peak of the pulse is additionally delayed compared to the time of passing the linear medium; the value of this delay significantly depends on the polarization of the incident pulse and achieves a maximum for incident pulses whose degree of ellipticity is equal to the ratio of the material constants characterizing the local and nonlocal nonlinear optical response of the medium. It seems promising to search for possible differences in relaxation times depending on the intensity of additions to the refractive indices of the right and left circularly polarized waves by investigating the time dependence of polarization characteristics at the output of the medium.     

Analysis of non-linear refractive index influences on four-wave mixing conversion efficiency in semiconductor optical amplifiers

In this paper, we have analyzed the influences of non-linear refractive index on the four-wave mixing (FWM) characteristics in semiconductor optical amplifiers (SOAs). It has been shown that the generated FWM signal characteristics can be modified due to the variation of non-linear refractive index of the SOA's medium. The wave propagation in the SOA has been modeled using the nonlinear propagation equation taking into account gain spectrum dynamics, gain saturation, which depends on carrier depletion, carrier heating, spectral hole-burning, group velocity dispersion, self-phase modulation and two photon absorption. Simulation of optical wave evolution in the SOA has been carried out using the finite-difference beam propagation method (FD-BPM) both in time and spectral domains. Our simulation results confirm that higher FWM conversion efficiency and lower time bandwidth product are achieved for higher absolute values of non-linear refractive index. Moreover, non-linear refractive index is more efficacious for high power propagated waves in SOAs. Finally, we have studied the modification of waveguide refractive index due to the propagation of optical pulses. We have also shown that when |n₂|=1 cm²/TW, refractive index variation is in the order of 10^?4 to 10^?7 for high and low power input pulses, respectively.